A method and apparatus are disclosed for generating accurate and precise ultrasonic images of biological materials or animate objects, such as the cornea and lens of the eye, and, in particular, to an ultrasonic scanning apparatus that can position its virtual center of curvature such that its ultrasonic transducer will emit pulses that reflect substantially perpendicularly from a curved specular surface of interest within the eye. This invention can allow real time imaging of a lens as it accommodates and can better enable researchers and ophthalmic surgeons to develop, fit, implant and diagnose performance of accommodative lenses.